Comparative study of TB-mBJ and GGA-PBE techniques on the electronic and optical characteristics of AlxGa1−xN alloys

• No comprehensive study compares GGA-PBE and TB-mBJ approximations for AlxGa1-xN alloys (x = 0, 0.25, 0.5, 0.75, 1). • GGA-PBE provides more reliable ε_1(0) outputs than TB-mBJ when compared to experimental results. • AlN results align better with GGA-PBE, while GaN results align more with TB-mBJ, indicating TB-mBJ is better for compounds with smaller energy gaps. • TB-mBJ is better for simulating AlGaN detectors in the solar-blind region, predicting greater absorption in the 10–100 nm range than GGA-PBE. • For AlxGa1-xN alloys, N 2p states (initial) and N 2s, Ga 4s states (final) are crucial for optical transitions at x = 0.25, 0.50, 0.75. • This study highlights the pros and cons of GGA-PBE and TB-mBJ for AlxGa1-xN alloys and recommends the best approximation based on application needs. The structural, electronic, and optical properties of AlN, GaN, and their ternary alloys Al x Ga 1− x N ( x = 0.25, 0.5, 0.75) in the zinc-blende structure have been investigated using density functional theory (DFT) calculations. This study comprehensively examines these properties, including the dielectric function within the random phase approximation, employing both GGA-PBE and TB-mBJ exchange–correlation functionals for comparative analysis. The results derived from these two approaches have been compared with each other and with available experimental and theoretical data. The findings for the electronic band structures, calculated using the Tran-Blaha modified Becke-Johnson (TB-mBJ) functional (4.880, 4.690, 4.014, 3.498, and 3.148 eV for x = 1, 0.75, 0.5, 0.25, 0), show good agreement with experimental band gaps for AlN and GaN. For the ternary alloys ( x = 0.25, 0.5, 0.75), where theoretical data using TB-mBJ are scarce, first-time predictions have been provided that demonstrate improved band gap values compared to other theoretical studies. The TB-mBJ approximation has been shown to significantly enhance the energy gap and shift the conduction bands to higher energies, resulting in a corresponding shift of the optical spectra. This shift leads to a decrease in the dielectric constant and refractive index. Additionally, the interband transitions responsible for the spectral features have been identified, with an analysis of the optical matrix elements revealing that the main peaks in the spectra are primarily driven by transitions from the N 2p states to the N 2s states.